I checked it to see how difficult it would be to do what you want and it seems to be working with something along these lines:
Themes/default/PortalShoutbox.template.php
<div class="shoutbox_input smalltext">
<input type="text" name="new_shout" id="new_shout_', $shoutbox['id'], '" class="shoutbox_input sp_float_left input_text"', $context['browser']['is_ie'] ? ' onkeypress="if (sp_catch_enter(event)) { sp_submit_shout(' . $shoutbox['id'] . ', \'' . $context['session_var'] . '\', \'' . $context['session_id'] . '\'); return false; }"' : '', ' />
<input type="submit" name="submit_shout" value="', $txt['sp_shoutbox_button'], '" class="sp_float_right button_submit" onclick="sp_submit_shout(', $shoutbox['id'], ', \'', $context['session_var'], '\', \'', $context['session_id'], '\'); return false;" />
</div>';
<div class="shoutbox_input smalltext">
<input type="submit" name="submit_shout" value="', $txt['sp_shoutbox_button'], '" class="button_submit" onclick="sp_submit_shout(', $shoutbox['id'], ', \'', $context['session_var'], '\', \'', $context['session_id'], '\'); return false;" style="float: right; width: 50px; height: 4.5em; outline: none;" />
<div style="margin-right: 60px;"><textarea name="new_shout" id="new_shout_', $shoutbox['id'], '" rows="3" style="width: 100%;"></textarea></div>
</div>';
It may need some fine tuning to make everything look perfectly sized and aligned, so good luck with that!